I'm working my way through the book Vector Calculus by Marden and Tromba and I've run into a bit of trouble on one of the problems (more like I'm clearly misunderstanding them but I'm not sure how). The question is as follows:
For $c:[a,b] \rightarrow \mathbb{R}^{3}$ we say $T(t) = c'(t)/||c'(t)||$ is the unit tangent to c. Show that $T'(t) \cdot T(t)=0$. What is $T'(t)$ in terms of c?
I think this formula will help you: $(a\cdot b)'= a'\cdot b+ a\cdot b'$.
And we know $T\cdot T=1$, a constant. What can we say about it?